The present invention relates to quantum well infrared photodetectors (QWIP) and, more particularly, to a simple way to optimize the geometry of a grating of a QWIP with respect to detection of light of a certain frequency, and the QWIP so designed.
QWIPs are devices for detecting medium and long wavelength infrared light. These devices rely on quantum wells, typically multiple quantum wells, to provide effective bandgaps that are narrower than can be achieved easily in homogeneous semiconductors. The theory and design of QWIPs is reviewed by B. F. Levine in "Quantum-well infrared photodetectors", Journal of Applied Physics vol. 74 no. 8 (Oct. 15, 1993), pp. R1-R81.
FIG. 1 is a schematic cross-section of a typical QWIP 10. QWIP 10 consists of parallel layers of a low-band-gap semiconductor 14 embedded in a relatively higher-band-gap semiconductor 12. For example, semiconductor 14 may be GaAs and semiconductor 12 may be Al.sub.x Ga.sub.1-x As. Ellipsis 16 indicates that there typically are many more layers than are shown in FIG. 1. In fact, a typical QWIP includes on the order of 50 periods of alternating layers 12 and 14. Layers 14 are quantum wells. This structure of alternating layers 12 and 14 is formed on a GaAs contact layer 13 above a GaAs substrate 15 and is capped by a GaAs contact layer 13'.
Many variations of the illustrative example of FIG. 1 exist. For example:
(a) Layers 12, 13, 13' and 15 may be Si, and layers 14 may be Si.sub.x Ge.sub.1-x. (b) Layers 12, 13, 13' and 15 may be InP, and layers 14 may be InGaAsP or InGaAs. (c) Layers 13, 13', 14 and 15 may be GaAs and layers 12 may be GaInP. (d) On a GaAs substrate, alternating barrier layers of AlGaAs and multilayer quantum wells; each quantum well consists of a sandwich of a central InGaAs layer between two GaAs layers; thin tunneling barrier layers of AlAs intervene between the quantum wells and the AlGaAs layers.
Other variations may be found in Levine's review article.
Because these semiconductors have indices of refraction, with respect to the propagation of infrared light, that are significantly greater than 1, infrared light incident from below on front surface 18 of QWIP 10 at almost any angle of incidence is refracted to propagate almost perpendicular to quantum wells 14. This makes the electric field vector of the light almost parallel to quantum wells 14. Unfortunately, it is only the component of the electric field perpendicular to quantum wells 14 that interacts with quantum wells 14. A common way to overcome this problem is to provide a two-dimensional grating 22, parallel to quantum wells 14, on back surface 20 of QWIP 10 to scatter the light, thereby causing the light to propagate within QWIP 10 in directions oblique and parallel to quantum wells 14 as well as perpendicular to quantum wells 14.
The geometry of grating 22 is defined by three parameters: pitch p, cavity width w, and cavity depth d. Pitch p define the lateral periodicities of grating 22. To enhance the performance of QWIP 10 with respect to infrared light of a frequency v, i.e., a free-space wavelength .lambda.=c/.nu. (where c is the speed of light in a vacuum) by promoting constructive interference of light scattered parallel to grating 22, p is set equal to the wavelength of the light inside QWIP 10, .lambda./n, where n is the index of refraction of semiconductor 13' with respect to light of frequency .nu.. Note that the infrared light for which the performance of QWIP 10 is optimized is defined herein in terms of frequency rather than in terms of wavelength to avoid confusion between the free-space wavelength of the light and the wavelength of the light within QWIP 10.
Two methods are known for selecting cavity depth d. The first is to use a simple rule of thumb, as taught by Chi et al. in U.S. Pat. No. 5,075,749. Light reflected from back surface 20 at an angle smaller than the critical angle of total internal reflection within QWIP 10 escapes from front surface 18. To suppress this, d is selected to promote destructive interference of light scattered perpendicular to grating 22. Specifically, to enhance the performance of QWIP 10 with respect to infrared light of frequency .nu., d is set equal to c/4n.nu., one-quarter of the wavelength of the light inside QWIP 10.
The second is to solve Maxwell's equations for the electromagnetic field inside QWIP 10 for a suite of values of d and to select the value of d that maximizes the quantum efficiency of QWIP 10. For example, J. Y. Andersson and L. Lundqvist, in "Grating-coupled quantum-well infrared detectors: theory and performance", Journal of Applied Physics vol. 71 no. 7 (Apr. 1, 1992) pp. 3600-3610, used the modal expansion method to calculate quantum efficiencies of a model QWIP 10 at various values of w and d to determine optimal values of w and d.
The regular geometry of grating 22 is not the only possible geometry. Levine et al., in U.S. Pat. No. 5,506,419, which is incorporated by reference for all purposes as if fully set forth herein, teach a QWIP grating with a pseudo-random geometry. In one variant of the pseudo-random geometry, the lateral dimensions of the grating cavities varies pseudo-randomly, while the depths of the cavities can have one of several values. These depths are selected as multiples of the quarter wavelength taught by Chi et al. in U.S. Pat. No. 5,075,749. It should be noted that the vector computation of Andersson and Lundqvist can be performed only for a grating such as grating 22 that has a regularly periodic geometry, and not for the pseudo-random geometries of Levine et al., U.S. Pat. No. 5,075,749.